Styles differ on how to hand various hand patterns. But, a possible scheme and possible solution recently occurred to me.
Suppose that you have agreed that a 3D response to a 1NT opening shows a GF hand with both minors. This is not my preferred approach, as I bid 2♠ first and then bid my stiff major at the three-level. But, suppose that this is your approach, such that showing the shortness is not easy.
One could flag the minor of preference (3♥ for clubs, 3♠ for diamonds) and then have Responder flag his short major (4♣ for hearts; 4D for spades). That works decently. However, Opener may want to have the ability to show a very strong acceptance immediately, reserving the 3M flags for hands not appropriate for the very strong acceptance.
When this occurs, I could imagine using an approach where Opener can show a hand suitable for slam acceptance in one of the minors, identifying the minor, and also indicating which splinter (which short minor) most interests him. In essence, an "empathetic splinter." The calls would then identify (1) the ideal short major empathized and (2) the minor of preference. To do this, it seems that one needs four calls.
My thought is to use 4♥ and 4♠ as empathetic splinters agreeing diamonds. Thus, either major flags diamonds and directly shows the location of the empathetic splinter. Thus, you might leap to 4♥ after 3D to show a hand with great minor cards and just small cards in hearts. You want partner to have a stiff heart to cover your lack of a heart control. 4♠ would show the same holding, but worthless spades.
To agree clubs, you flag clubs by bidding one of the minors (4♣ or 4D), flagging the "empathetic splinter" major (4♣ for hearts, 4D for spades). So, 4♣ would show club support and small cards in hearts; 4D would show club preference and small cards in spades.
The reason for this approach is to keep club agreement lower, because you need more space for RKCB when the agreed suit is clubs. 4NT after 4♠ (spade empathetic splinter, diamonds agreed) is still troubling, but at least two responses are at or below 5D.
This same type of approach might be used in other situations, where you have compound flagging going on. In a non-slam sequence, I have used a similar "compound flagging" in a sense. Imagine 1♣-P-1♥-1NT(sandwich)-P-? To me, it makes sense for Advancer to "compound flag." The two messages are "what suit to name as trumps" and "what suit to lead." For, you might have Kx-xxxx in the two suits, where you want a lead in the one suit but to declare the other. So, you bid the suit if you want the lead but flag the suit if you want the other lead. Thus, 2D would "flag" diamonds for lead and for declaring, whereas 2♣ would flag diamonds for declaring but flag spades for lead. 2♠ would flag spades for lead and for declaring, whereas 2♥ would flag spades for declaring but flag clubs for lead.
You might also look for splinter flag situations, where you use four bids to distinguish (1) what is the short suit and (2) what suit are you supporting.
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